Question

Find A:B:C if A:B=1/4:1/5 and B:C=1/7:1/6.
Please show steps.

Answer 1

Start by making the common component equal in each condition.
\[(\frac{1}{4}:\frac{1}{5}) \times \frac{1}{7}=\frac{1}{28}:\frac {1}{35}\]\[(\frac{1}{7}:\frac{1}{6}) \times \frac {1}{5} =\frac {1}{35}:\frac{1}{30}\]
Leaving you with:\[A:B:C = \frac{1}{28}:\frac{1}{35}:\frac{1}{30}\]

Answer 2

But aren't fractions in terms of ratios have to be converted to whole numbers before doing a question?

Answer 3

Valid question I did not believe a conversion was needed, however at the moment I do not have an answer and as such you cannot trust my response until it can be proven one way or another. I apologize.

Answer 4

No, in that way, what you have done is absolutely correct. It's just that this question is from my school math book and the answers are at the back, where it says the answer to this question is 15:12:14. I'm puzzled as to how they've got this.

Answer 5

AH. \[\frac{1}{4}:\frac{1}{5} cross \space multiply = 5:4 \space (new A:B)\]
\[\frac{1}{7}:\frac{1}{6} cross \space multiply = 6:7 \space (new B:C)\]
Same process now applies, balance the common component
\[(5:4) \times 3 = 15:12\]\[(6:7) \times 2=12:14\]
A:B:C = 15:12:15

Answer 6

Thank you so much! God, i can't believe it's that simple. Thanks a lot. :)

Answer 7

Glad I could help. :)